This is an orthogonal generalization of \(k\) -MedianOut to ensure a certain notion of fairness in the solution (see [1]}). Suppose the set of points \(X\)  is partitioned into \(\ell \)  different colors \(X_1 \uplus X_2 \uplus \ldots \uplus X_\ell \) . We are also given the corresponding number of outliers \(m_1, m_2, \ldots , m_\ell \) . The goal is to find a set of at most facilities \(C\)  to minimize the connection cost of all except at most \(m_t\)  outliers from each color class \(X_t\) , i.e., we want to minimize the cost function: \(\sum _{t = 1}^\ell \mathsf {cost}_{m_t}(X_t, C)\) . This follows a generalizations of the well-known \(k\) -Center problem introduced by Badnyapadhyay et al. [2]} and studied in [3]}, [1]} , called Colorful \(k\) -Center. Similar generalization of Facility Location has also been studied in [5]}.
